CN110556871B - Aggregation equivalence method for large-scale photovoltaic power generation system based on structure keeping method - Google Patents
Aggregation equivalence method for large-scale photovoltaic power generation system based on structure keeping method Download PDFInfo
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Abstract
The invention provides a large-scale photovoltaic power generation system aggregation equivalence method based on a structure keeping method, which comprises the following steps of: establishing a detailed mathematical model of a two-stage photovoltaic power generation system, which comprises a mathematical model of a photovoltaic array, an average model of a front-stage Boost circuit, an average model of a rear-stage grid-connected inverter, an equivalent model of a transformer, and a mathematical model of a maximum power point tracking controller and a grid-connected voltage and current controller; obtaining the relation between a detailed model of the large-scale photovoltaic power generation system and an equivalent model state variable according to the energy conservation relation between magnetic field energy, electric field energy and generalized potential energy existing in the photovoltaic power generation system; determining the current and voltage relation between the detailed model and the equivalent model according to the same active power output and power grid access mode between the detailed model and the equivalent model; and (3) providing an equivalent parameter calculation method of the aggregate equivalent model by using a capacity weighting method and comparing state equations among different models. The method has the advantages that on the basis of simplifying the order-reducing model, the aggregation model keeps the same circuit and control structure as the original photovoltaic power generation system, and meanwhile, the accurate and reliable calculation method is provided for solving equivalent parameters of a photovoltaic array, a Boost circuit, an inverter, an output filter, a transformer, a maximum power point tracking controller and a grid-connected voltage and current controller in the aggregation equivalent model.
Description
Technical Field
The invention belongs to the technical field of new energy grid-connected power generation, and particularly relates to a method for calculating a dynamic aggregation equivalent model and equivalent parameters of a large-scale photovoltaic power generation system based on a structure storage method.
Background
Photovoltaic power generation is considered to advance an important way of energy conversion and coping with environmental challenges due to the ready availability of photovoltaic resources and their low cost, non-polluting nature. Generally, in order to output sufficient active power, an actual photovoltaic power station mostly adopts a mode of connecting a plurality of photovoltaic inverters in parallel in a cluster to be connected into a power distribution network for operation, so that the photovoltaic power station is a large-scale high-order system. The simulation analysis of the large-scale photovoltaic system consumes longer time and occupies larger calculation space. In addition, due to the large scale of the system, it is very difficult to study the operation characteristics of the large-scale multi-parallel photovoltaic power generation system in different environments, and it is difficult to evaluate the dynamic stability of the large-scale photovoltaic system when faults and small disturbances occur.
Therefore, in order to simplify the analysis of the large-scale system and quickly evaluate the dynamic response capability of the large-scale system, it is necessary to establish a dynamic aggregation equivalent model of the large-scale system. The dynamic equivalent model of the large-scale photovoltaic system is actually a simplified reduced-order equivalent model, has the same output power and consistent dynamic response capability as the actual detailed model, and can realize accurate replacement of the large-scale photovoltaic system under the conditions of steady state and transient state by using less computation space and analysis time.
At present, the research aiming at the equivalent model of a large-scale photovoltaic system mainly focuses on a clustering method of photovoltaic inverters, namely, a plurality of photovoltaic inverters with the same dynamic characteristic use different clustering algorithms to perform clustering equivalence on the photovoltaic inverters. The patent CN106054665A obtains the sensitivity of preset control parameters of the photovoltaic inverter, and performs clustering and clustering equivalence on the photovoltaic inverter according to a K-means clustering algorithm, but does not introduce a method for calculating equivalent parameters in multiple equivalence models after the inverter is clustered. In patent CN106451418A, the distance between unit impulse response curves corresponding to each photovoltaic power generation unit is used as a clustering index, a K-means algorithm is used to perform online clustering on a photovoltaic power station model, and an online clustering equivalence model of the photovoltaic power station is established according to the actual output of each photovoltaic power generation unit, but the calculation of equivalence parameters only includes equivalent parameters of active and reactive control links of the inverter. In patent CN109638892A, an equivalent model of a photovoltaic power station is obtained by a fuzzy clustering algorithm, standardized processing is performed by determining a clustering index of a photovoltaic power generation unit, a membership matrix is initialized, and an equivalent aggregation parameter of the photovoltaic power station is obtained according to a clustering result.
In summary, establishing a detailed large-scale photovoltaic power generation system aggregate equivalent model including a photovoltaic array, a preceding stage Boost circuit, an inverter, a filter, a transformer, a maximum power point tracking controller, and a grid-connected current controller, and a corresponding equivalent parameter solving method are technical problems that need to be solved by those skilled in the art at present.
Disclosure of Invention
The invention aims to provide an aggregation equivalent model of a large-scale photovoltaic power generation system and a detailed equivalent parameter solving method for establishing the aggregation equivalent model.
The technical scheme of the invention is as follows: the aggregation equivalent model of the large-scale photovoltaic power generation system based on the structure preservation method is characterized by comprising a plurality of photovoltaic power generation units, a photovoltaic array inside each unit, a front-stage Boost booster circuit, a rear-stage grid-connected inverter, a transformer, a maximum power point tracking controller and a detailed model including a grid-connected voltage and current controller, a dynamic aggregation equivalent model with the same structure and a detailed equivalent parameter solving method of each component in the aggregation model.
Further, establishing a detailed mathematical model of the two-stage photovoltaic power generation system, wherein the detailed mathematical model comprises a mathematical model of a photovoltaic array, an average model of a preceding stage Boost circuit, an average model of a grid-connected inverter, an average model of a filter, a simplified model of a transformer, a mathematical model of a maximum power point tracking controller, a voltage outer ring of the grid-connected inverter and a current inner ring controller model;
furthermore, according to magnetic field energy, electric field energy and generalized potential energy existing in the photovoltaic power generation system, an energy conservation relation between any two parallel photovoltaic power generation units can be obtained, and further a state variable relation between the detailed model and the equivalent model is deduced;
further, according to the fact that the total active power output of the detailed model and the equivalent model is unchanged, a current relation between the detailed model and the equivalent model is established, according to the fact that the detailed model and the equivalent model are connected into a power distribution network with the same voltage class through the same power transmission line, and the parallel photovoltaic power generation units are controlled synchronously without errors, the voltage relation between the detailed model and the equivalent model is obtained;
further, a structure storage method is utilized to popularize a mathematical model of the two-stage photovoltaic power generation system to establish a state equation of a polymerization equivalent model;
further, equivalent parameters of the equivalent photovoltaic array are calculated by using a capacity weighting method, a state equation of the detailed model and the equivalent model is compared according to a state variable relation, a current relation and a voltage relation between the detailed model and the equivalent model, an aggregation parameter calculation method of a Boost circuit, a grid-connected inverter, a filter, a transformer, a maximum power point tracking controller and a grid-connected voltage and current controller in the equivalent model is obtained, and an aggregation equivalent model of the large-scale photovoltaic system is established.
The invention has the beneficial effects that:
1. the invention establishes an aggregation equivalent model of a large-scale photovoltaic power generation system by using a structure storage method, wherein the aggregation equivalent model comprises a photovoltaic array, a front-stage Boost circuit, a grid-connected inverter, an output filter, a transformer, a maximum power point tracking controller, grid-connected voltage and current control and the like, and a detailed equivalent model and equivalent parameter calculation method is provided.
2. According to the method, the energy conservation relation among the magnetic field energy, the electric field energy and the generalized potential energy in the two-stage photovoltaic power generation system is established, and the mathematical relation which is satisfied by the state variables between any two photovoltaic power generation units is deduced, so that the method for calculating the equivalent parameters in the aggregation equivalent model has higher accuracy and reliability.
3. The aggregation equivalent model established by the invention has the steady-state and dynamic response capability consistent with that of a large-scale photovoltaic power generation system, can capture the operation characteristics and the dynamic response process of the large-scale photovoltaic power generation system when the power grid is in a symmetrical and asymmetrical fault transient state, and realizes accurate replacement of the large-scale system by using a simplified reduced-order model.
Drawings
FIG. 1 is a flow chart of an equivalent method for aggregation of a large-scale photovoltaic power generation system based on structure preservation according to the present invention;
FIG. 2 is a block diagram of a main circuit and control of a two-stage photovoltaic power generation system according to the present invention;
FIG. 3 is a simplified circuit and control block diagram for modeling a two-stage photovoltaic power generation system according to the present invention;
FIG. 4 is a schematic diagram of a detailed model of a large-scale photovoltaic system of the present invention;
FIG. 5 is a schematic diagram of an aggregate equivalence model of a large-scale photovoltaic system according to the present invention;
FIG. 6 is an output active power curve of the large-scale photovoltaic system detailed model and the aggregation equivalent model under the grid fault transient state;
fig. 7 is an output reactive power curve of the large-scale photovoltaic system detailed model and the aggregation equivalent model under the transient state of the power grid fault.
Detailed Description
The embodiments of the present invention will be described in detail below with reference to the accompanying drawings: the present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
In this embodiment, as shown in fig. 1, a large-scale photovoltaic power generation system aggregation equivalent method based on a structure preservation method is performed according to the following steps:
s1: a detailed mathematical model of a two-stage photovoltaic power generation system is established, and as shown in fig. 2, the two-stage photovoltaic power generation system comprises a photovoltaic array, a front-stage Boost circuit, a grid-connected inverter, a filter, a transformer, a maximum power point tracking controller, a grid-connected inverter voltage outer loop and a current inner loop controller.
Specifically, to solve the problem of model complexity caused by different voltage levels at two ends of the transformer, as shown in fig. 3, after the secondary side parameter of the transformer is converted to the primary side of the transformer, the transformer is simplified to be an equivalent inductor, the output filter can be regarded as an LCL filter, and similarly, L is a L filter g ，R g To equivalent grid impedance, v, converted to the primary side of the transformer g For equivalent grid voltage at the primary side of the transformer, the two-stage photovoltaic power generation system is connected to an equivalent grid through the grid impedance converted to the primary side.
Further, the step S1 of establishing a detailed mathematical model of the two-stage photovoltaic power generation system specifically includes the following substeps:
s11, a mathematical model of the photovoltaic array:
photovoltaic array output voltage v pv And an output current i pv The relationship between them is:
in the formula: n is a radical of s And N p The number of series connection and parallel connection of the photovoltaic cells are respectively, n is an ideal factor of the diode, k is a Boltzmann constant, T is the temperature of a p-n junction of the diode, q is a unit charge constant, and I sc Short-circuit current for photovoltaic arrays, I 0 Is the saturation current of the diode.
The voltage and current output by the photovoltaic array are mainly determined by the serial number and the parallel number of the photovoltaic cells, so that the linearized mathematical model of the photovoltaic array is as follows:
in the formula: I.C. A pv0 Representing the steady-state operating point, K, of the output current of the photovoltaic array pv Is a reaction of pv0 A function of interest.
S12, an average model of a preceding stage Boost circuit:
the preceding stage Boost circuit rises to press the function and is used for realizing the maximum power point tracking control of photovoltaic array among the two-stage type photovoltaic power generation system, and its average model is:
in the formula: c pv Is a smoothing capacitor of a preceding stage circuit, L is a Boost circuit energy storage inductor, i L D is the duty ratio of the Boost circuit, v is the current flowing through the energy storage inductor dc Is a DC bus voltage, C dc Is a DC bus capacitor i dc Is the current flowing into the inverter.
S13, average model of grid-connected inverter:
the three-phase grid-connected inverter adopts a PWM modulation mode, and the average model is as follows:
i dc ＝m d i fd +m q i fq (6)
in the formula: m is a unit of d ，m q The components of the modulation degree of the inverter under the d and q axes of the synchronous rotation coordinate system i fd ，i fq ，v sd ，v sq Are respectively filteringAnd d and q axis components of the current and the output voltage of the inverter corresponding to each other in a synchronous rotating coordinate system.
S14, output filter and mathematical model of transformer
The current output by the inverter is connected into the transformer through the LC filter and then connected into a grid connection point of a system, so that in order to avoid the problem of complex parameter calculation caused by different voltage levels, the parameters of the transformer and a power grid are converted to the primary side, the transformer is simplified into an equivalent inductor, the whole of the filter and the transformer can be regarded as an LCL filter, and the mathematical model is as follows:
in the formula, L f Is a filter inductance, i f For the current through the filter inductance, i fd 、i fq The components of the filter inductance current in d and q axes of a synchronous rotating coordinate system respectively, C f Is a filter capacitance, v cf Is the filter capacitor voltage v cfd 、v cfq Respectively a filter capacitor voltage atComponent of d and q axes in synchronous rotation, R f 、R c Parasitic resistances, L, of filter inductance and filter capacitance, respectively t Is an equivalent inductance of a transformer, v pcc To grid point voltage, v pccd 、v pccq Respectively d-axis component and q-axis component, i, of the grid-connected point voltage in a synchronous rotation coordinate system t For the current through the equivalent inductance of the transformer, i td 、i tq The equivalent inductive current of the transformer is respectively the d-axis component and the q-axis component under a synchronous rotating coordinate system, and omega is the angular frequency of a power grid.
S15, a maximum power point tracking controller and a mathematical model of a grid-connected voltage and current controller:
the maximum power point tracking controller is used for generating the duty ratio of the preceding stage Boost circuit and the photovoltaic output voltage v pv Voltage value v corresponding to maximum power point mp And comparing, inputting the error signal into a PI controller, and generating the duty ratio d of the preceding stage Boost circuit, wherein the mathematical expression is as follows:
in the formula: k is a radical of formula po 、k io Proportional gain and integral gain of the voltage outer loop PI controller are respectively, and s is a Laplace operator.
The controller of the grid-connected inverter consists of a voltage outer ring and a current inner ring, wherein the voltage outer ring is used for stabilizing the voltage v of the direct-current bus dc The current inner ring is used for improving the dynamic response of grid-connected current and ensuring that the grid-connected current is connected in a unit factor mode, and the mathematical models of the voltage outer ring and the current inner ring are as follows:
in the formula:
is the d-axis and q-axis current reference values under the synchronous rotation coordinate system,
is the reference value of the DC bus voltage, k pdc 、k idc Respectively, the proportional and integral coefficients, m, of the voltage outer loop PI controller d 、m q The modulation degrees, k, of the inverter under d and q axes in a synchronous rotation coordinate system pd 、k id Respectively is the proportional coefficient and the integral coefficient k of a d-axis current inner loop PI controller under a synchronous rotating coordinate system pq 、k iq The proportional and integral coefficients of the q-axis current inner loop PI controller under the synchronous rotation coordinate system are respectively.
S2, determining magnetic field energy, electric field energy and generalized potential energy existing in any two parallel-connected two-stage photovoltaic power generation units, wherein as shown in FIG. 4, the large-scale photovoltaic power generation system is connected in parallel through n photovoltaic power generation units and then is connected into a power grid through a step-up transformer, and each photovoltaic power generation unit and the two-stage photovoltaic power generation system have the same main circuit and control link;
specifically, the energy corresponding relation of any two parallel photovoltaic power generation units is established according to the law of conservation of energy, and the energy corresponding relation is specifically expressed as follows:
in the formula: t represents magnetic field energy, V represents electric field energy, k is a constant, U represents generalized potential energy in the photovoltaic system, wherein the generalized potential energy of the photovoltaic system is composed of alternating current power supply output energy, direct current power supply input energy and energy consumed by resistors in the system, and digital subscripts 1 and 2 are used for distinguishing main circuit parameters of any two photovoltaic power generation units connected in parallel.
The relationship between the state variables can be obtained from the energy conservation relationship in equation (19), which is expressed as follows:
in the formula: k is a radical of formula L The numerical subscripts 1 and 2 are used for distinguishing main circuit parameters of any two photovoltaic power generation units connected in parallel.
S3, determining a current relation between the detailed model and the equivalent model according to the fact that the detailed model of the large-scale photovoltaic system and the aggregation equivalent model have the same output power; according to the detailed model and the equivalent model, a power distribution network with the same voltage class is accessed through the same power transmission line, and a first transformer side and a second transformer side in each photovoltaic power generation unit have the same voltage class, so that a voltage relation between the detailed model and the equivalent model is obtained;
specifically, because the output power of the photovoltaic power generation system is determined by the grid-connected current, according to the output power relationship between the detailed model and the equivalent model, the power of the equivalent model should be the sum of the power of each photovoltaic power generation unit in the detailed model, and the current relationship between the equivalent model and the detailed model can be further obtained, and the mathematical expression is as follows:
in the formula: i.e. i pveq Is the output current, i, of the photovoltaic array in the equivalence model Leq For storing inductor current, i, of Boost circuit in equivalent model dceq For the inverter input current, i, in the equivalence model feq For the current, i, of the filter inductor in the equivalent model teq Is the current i flowing through the equivalent inductance of the transformer in the equivalent model pvl 、i Ll 、i dcl 、i fl 、i tl Respectively including the output current of a photovoltaic array in the first parallel power generation unit in a large-scale photovoltaic system, the energy storage inductive current of a Boost circuit, the input current of an inverter, the inductive current of a filter and the equivalent inductive current of a transformer, wherein l is 1-any number within the range of n, n being the number of parallel power generating units in a large scale photovoltaic system.
According to the detailed model and the equivalent model, the same voltage class power distribution network is accessed through the same power transmission line, the first side and the second side of the transformer in each photovoltaic power generation unit have the same voltage class, the voltage relation between the equivalent model and the detailed model is obtained, and the mathematical expression is as follows:
v pcceq ＝v pccl (22)
in the formula, v pcceq Voltage of point of connection in representative aggregation equivalent model, v pccl The grid-connected point voltage of the first power generation unit in the large-scale photovoltaic power generation system.
According to the voltage proportional relation in the formula (20), the rest voltage relation between the polymerization model and the detailed model can be obtained, and the mathematical expression thereof is as follows:
v pveq ＝v pvl ,v dceq ＝v dcl ,v cfeq ＝v cfl · (23)
in the formula: v. of pveq Is the output voltage, v, of the photovoltaic array in the equivalence model dceq Is the DC bus voltage v in the equivalent model cfeq For the filter capacitor voltage, v, in the equivalent model pvl 、v dcl 、v cfl The voltage is respectively the photovoltaic array output voltage, the direct current bus voltage and the filter capacitor voltage in the first parallel power generation unit in the large-scale photovoltaic system.
And S4, keeping the topological structures consistent, popularizing the two-stage photovoltaic power generation system mathematical model obtained in the S1 to establish a complete state equation of the aggregation equivalent model, wherein the aggregation equivalent model is an independent two-stage photovoltaic power generation system as shown in FIG. 5, the aggregation equivalent model has the same main circuit and control circuit structure as a large-scale photovoltaic power generation system, and the state equation of the aggregation equivalent model is obtained through popularization according to the two-stage photovoltaic power generation system state equation established in the step S1, and the method specifically comprises the following substeps:
s41, a preceding stage Boost circuit of the aggregation model, an inverter and a mathematical model of an output filter:
in the formula: c pveq Is a preceding stage filter capacitor in an equivalent model, L eq For the Boost circuit energy storage inductor in the equivalent model, d eq Is the duty ratio of Boost circuit in equivalent model, C dceq Is a DC bus capacitance, L, in the equivalent model feq Is a filter inductance in an equivalent model, S abceq As a switching function of an equivalent inverter, C feq As filter capacitance in the equivalent model, R feq Is parasitic resistance, R, of filter inductor in equivalent model ceq Is the parasitic resistance, L, of the filter capacitor in the equivalent model teq The equivalent inductance of the transformer in the equivalent model.
S42, controller model of aggregation model
By popularizing the formula (15), the maximum power point tracking controller model of the aggregate equivalent model can be obtained, and the mathematical expression of the model is as follows:
d eq ＝k poeq (v mpeq -v pveq )+k ioeq ∫(v mpeq -v pveq )dt (25)
in the formula, k poeq Represents the equivalent proportionality coefficient, k, of the Boost circuit PI controller in the equivalent model ioeq Represents the equivalent integral coefficient, v, of the PI controller of the Boost circuit in the equivalent model mpeq And the maximum voltage corresponding to the maximum power point in the equivalent model.
Similarly, a grid-connected voltage and current controller model in the aggregate equivalence model can be obtained, and the mathematical expression of the grid-connected voltage and current controller model is as follows:
in the formula:
are d-axis and q-axis current reference values i in the equivalent model respectively tdeq 、i tqeq Are respectively d-axis components and q-axis components of equivalent inductance current of the transformer in the equivalent model,
is a DC bus voltage reference value, k, in the equivalent model pdceq 、k idceq Respectively is the proportional coefficient and the integral coefficient m of a voltage outer ring PI controller in the equivalent model deq 、m qeq Modulation degrees, k, of d and q axes of the inverter synchronous rotation coordinate system in the equivalent model pdeq 、k ideq Proportional and integral coefficients k of a d-axis current inner loop PI controller in the equivalent model respectively pqeq 、k iqeq And the proportional coefficient and the integral coefficient of the q-axis current inner loop PI controller in the equivalent model are respectively.
And S5, calculating equivalent parameters of the equivalent photovoltaic array by using a capacity weighting method, comparing state equations of the detailed model and the equivalent model according to the state variables, the voltage and the current relations between the detailed model and the equivalent model obtained in the S2 and the S3, obtaining a calculation formula of the aggregation parameters of a Boost circuit, a grid-connected inverter, a filter, a transformer, a maximum power point tracking controller and a grid-connected voltage and current controller in the equivalent model, and establishing an aggregation equivalent model of the large-scale photovoltaic system.
Specifically, because the output voltage of the photovoltaic array is mainly determined by the serial number, the output current is mainly determined by the parallel number, and the output voltage of the photovoltaic array in the aggregation model and the detailed model is unchanged, and the output current of the photovoltaic array in the equivalent model is the sum of the output currents of the parallel photovoltaic arrays in the detailed model, the equivalent parameter of the equivalent photovoltaic array calculated by adopting a capacity weighting method is calculated by the following steps:
N seq ＝N sl 
in the formula N seq Is the number of series connection of equivalent photovoltaic arrays, N peq Is the parallel number of the equivalent photovoltaic array. Namely, the serial number of the equivalent photovoltaic arrays in the aggregation equivalent model is the same as that of the photovoltaic arrays in the detailed model, and the parallel number of the equivalent photovoltaic arrays is the sum of the parallel number of the photovoltaic arrays in the detailed model.
Furthermore, according to the mathematical model of the two-stage photovoltaic power generation system, mathematical models of a front stage boost circuit, an inverter and a filter in any parallel photovoltaic power generation unit can be obtained, and the mathematical expressions are as follows:
in the formula: c pvl Is the preceding stage filter capacitor, L, of the first parallel power generation unit in a large-scale photovoltaic system l Energy storage inductor d of Boost circuit of the first parallel power generation unit in large-scale photovoltaic system l Is the duty ratio of Boost circuit in equivalent model, C dcl Is the direct current bus capacitor, L of the first parallel power generation unit in a large-scale photovoltaic system fl Is the filter inductance of the first parallel power generation unit in a large-scale photovoltaic system S abcl For the switching function of the first parallel power generating unit in large-scale photovoltaic systems, C fl Is the filter capacitor R of the first parallel power generation unit in a large-scale photovoltaic system fl Is the filter inductance parasitic resistance R of the first parallel power generation unit in a large-scale photovoltaic system cl Is the filter capacitance parasitic resistance, L, of the first parallel power generation unit in a large-scale photovoltaic system tl The equivalent inductance of the transformer of the first parallel power generation unit in the large-scale photovoltaic system.
The state equations of a Boost circuit, an inverter and a filter of n photovoltaic power generation units connected in parallel are superposed, and the mathematical expression is as follows:
further, assuming that the Boost circuits in the photovoltaic power generation units are not different, the inverter controls the carrier waves with the same frequency, and the inverter is connected to the power distribution network with the same voltage level, and the photovoltaic array output voltage, the direct-current bus voltage and the grid-connected point voltage in the photovoltaic power generation units and the equivalent model are the same, so the duty ratio of the Boost circuits in each parallel power generation unit and the equivalent model of the detailed model is the same, the switching function of the inverter is the same, and the mathematical expression is as follows:
S abceq ＝S abcl ,d eq ＝d l (32)
from the result of equation (32), comparing the left side of equation (24) and equation (31), the method for calculating the equivalent inductance and equivalent capacitance in the equivalent model is known, and the mathematical expression is:
by using the obtained equivalent capacitance and equivalent inductance calculation formula and comparing the right terms of the formula (24) and the formula (31), the calculation method of the equivalent resistance in the equivalent model can be known, and the mathematical expression is as follows:
s53, method for calculating equivalent parameters of transformer in equivalent model
In order to keep the primary side voltage of the transformer unchanged after equivalence, the equivalent transformer capacity in the equivalent model is the sum of the capacities of all transformers in the detailed model, and the mathematical expression is as follows:
in the formula: s. the teq For transformation in equivalent modelsVolume of the device, S tl The capacity of the transformer of the first parallel power generation unit in the large-scale photovoltaic power generation system.
S54, a method for calculating equivalent parameters of the controller in the equivalent model comprises the following steps:
the equivalent model and the detailed model have the same main circuit structure and control circuit structure, the output voltage of the photovoltaic array and the duty ratio of the Boost circuit in the equivalent model are the same as those of the detailed model, and the equivalent parameter calculation method for obtaining the maximum power point tracking PI controller in the equivalent model by comparing the formula (15) and the formula (25) is as follows:
k poeq ＝k pol ,k ioeq ＝k iol (36)
in the formula: k is a radical of formula pol Proportional coefficient k of a Boost circuit PI controller of the first parallel power generation unit in a large-scale photovoltaic system iol The integral coefficient of a Boost circuit PI controller of the first parallel power generation unit in a large-scale photovoltaic system.
According to the claim 4, the detailed model and the equivalent model have the same direct-current bus voltage, and the detailed model and the equivalent model have the same voltage reference signal, in order to ensure that the detailed model and the equivalent model have the same active power, a d-axis current reference value signal representing the active current in the equivalent model is the sum of d-axis current reference values in the detailed model, and the mathematical expression of the d-axis current reference value signal is as follows:
in the formula:
the d-axis current reference signal of the l-th power generation unit in the large-scale photovoltaic system.
According to the result of the equation (37), comparing the equation (16) with the equation (26), the equivalent parameter calculation method of the inverter voltage outer loop in the equivalent model can be obtained, and the mathematical expression is as follows:
in the formula: k is a radical of formula pdcl Is the proportionality coefficient k of the voltage outer loop PI controller of the first parallel power generation unit in a large-scale photovoltaic system idcl The integral coefficient of the voltage outer loop PI controller of the ith parallel power generation unit in the large-scale photovoltaic system.
The detailed model and the equivalent model have the same active power, and parameters of the equivalent current inner-loop controller are calculated by adopting a capacity weighting method. In particular, a capacity weighting factor γ is defined l The mathematical expression is as follows:
in the formula: p l The active output, P, of the first power generation unit in the large-scale photovoltaic power generation system sum The total active power output of the large-scale photovoltaic system.
Further, an equivalent PI parameter calculation method of the current inner ring controller in the equivalent aggregation model can be obtained, and the mathematical expression of the method is as follows:
in the formula: k is a radical of formula pdl D-axis current inner loop PI controller proportionality coefficient k representing the first parallel power generation unit in large-scale photovoltaic system idl D-axis current inner loop PI controller integral coefficient k representing the first parallel power generation unit in a large-scale photovoltaic system pql Q-axis current inner loop PI controller proportionality coefficient representing the first parallel power generation unit in large-scale photovoltaic system，k iql And the integral coefficient of the q-axis current inner loop PI controller of the ith parallel power generation unit in the large-scale photovoltaic system is represented.
And (5) integrating the steps S1-S5 to obtain the calculation formulas of all equivalent parameters in the large-scale photovoltaic system aggregation equivalent model, and accordingly, establishing the large-scale photovoltaic system aggregation equivalent model.
Further, a detailed model and an aggregation equivalent model of the large-scale photovoltaic system are subjected to simulation analysis respectively, the same continuous symmetrical and asymmetrical power grid faults are set at the grid-connected points of the large-scale photovoltaic system and the aggregation equivalent model respectively, an active power curve and a reactive power curve output by the large-scale photovoltaic system detailed model and the equivalent model are detected, and consistency verification of the detailed model and the aggregation equivalent model under the transient state of small disturbance and power grid faults is carried out, as shown in fig. 6 and 7 respectively.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other changes and modifications to the disclosed embodiments without departing from the spirit and scope of the invention.
Claims (5)
1. The large-scale photovoltaic power generation system aggregation equivalence method based on the structure keeping method is characterized by comprising a plurality of photovoltaic power generation units, photovoltaic arrays inside each unit, a front-stage Boost circuit, a rear-stage grid-connected inverter, a transformer, a maximum power point tracking controller, detailed models including a grid-connected voltage and current controller, aggregation equivalence models with the same structure, equivalent photovoltaic arrays inside, equivalent Boost circuits, equivalent grid-connected inverters, equivalent transformers, equivalent maximum power point tracking controllers and equivalent grid-connected voltage and current controllers, and comprising the following steps:
s1, establishing a detailed time domain mathematical model of a two-stage photovoltaic power generation system, wherein the detailed time domain mathematical model comprises a mathematical model of a photovoltaic array, an average model of a preceding stage Boost circuit, an average model of a grid-connected inverter, an average model of a filter, a simplified model of a transformer, a mathematical model of a maximum power point tracking controller, a voltage outer ring of the grid-connected inverter and a current inner ring controller model;
s2, determining magnetic field energy and electric field energy existing in any two parallel two-stage photovoltaic power generation units, establishing an energy relation between the magnetic field energy and the electric field energy of any two parallel photovoltaic power generation units and generalized potential energy by utilizing an energy conservation law, and deducing a mathematical relation of state variables between any two photovoltaic power generation units;
s3, keeping the output active power of the aggregation equivalent model unchanged, and determining a current relation between the detailed model and the equivalent model; assuming that the control of each parallel photovoltaic power generation unit is synchronous and no error exists, the detailed model and the equivalent model are connected into the power distribution network with the same voltage class through the same power transmission line, and the voltage relation between the detailed model and the equivalent model is obtained;
s4, popularizing the mathematical model of the two-stage photovoltaic power generation system obtained in the S1 to establish a state equation of a polymerization equivalent model;
s5, calculating equivalent parameters of the equivalent photovoltaic array by using a capacity weighting method, comparing state equations of the detailed model and the equivalent model according to the relation between the state variables of the detailed model and the equivalent model obtained in S2 and S3 and the voltage and current relation between the obtained detailed model and the equivalent model to obtain an aggregation parameter calculation formula of a Boost circuit, a grid-connected inverter, a filter, a transformer, a maximum power point tracking controller and a grid-connected voltage and current controller in the equivalent model, and establishing an aggregation equivalent model of the large-scale photovoltaic system;
in the step S1, a detailed mathematical model of a two-stage photovoltaic power generation system is established, and the detailed mathematical model comprises the following specific steps:
s11, a mathematical model of the photovoltaic array:
photovoltaic array output voltage v pv And an output current i pv The relationship between them is:
in the formula: n is a radical of s And N p The number of series connection and the number of parallel connection of the photovoltaic cells are respectively, n is an ideal factor of the diode, k is a Boltzmann constant, T is the temperature of a p-n junction of the diode, q is a unit charge constant, I sc Short-circuit current for photovoltaic arrays, I 0 Is the saturation current of the diode;
the voltage and current output by the photovoltaic array are mainly determined by the serial number and the parallel number of the photovoltaic cells, so that the linearized mathematical model of the photovoltaic array is as follows:
in the formula: i is pv0 Representing the steady-state operating point, K, of the output current of the photovoltaic array pv Is a reaction of pv0 A function of interest;
s12, an average model of a preceding stage Boost circuit:
the preceding stage Boost circuit rises to press the function and is used for realizing the maximum power point tracking control of photovoltaic array among the two-stage type photovoltaic power generation system, and its average model is:
in the formula: c pv Is a flat wave capacitor of a preceding stage circuit, L is a Boost circuit energy storage inductor, i L D is the duty ratio of Boost circuit, v is the current flowing through the energy storage inductor dc Is a voltage of the direct-current bus,C dc is a DC bus capacitor, i dc Is the current flowing into the inverter;
s13, average model of grid-connected inverter:
the three-phase grid-connected inverter adopts a PWM modulation mode, and the modulation degree m of the inverter in d and q axes of a synchronous rotating coordinate system is determined d 、m q Establishing an average model of the inverter, wherein the mathematical expression of the average model is as follows:
i dc ＝m d i fd +m q i fq (6)
in the formula: i.e. i fd 、i fq 、v sd 、v sq D-axis components and q-axis components corresponding to the filter current and the inverter output voltage under a synchronous rotating coordinate system respectively;
s14, an output filter and a mathematical model of the transformer:
the current output by the inverter is connected into the transformer through the LC filter and then connected into a grid connection point of a system, so that in order to avoid the problem of complex parameter calculation caused by different voltage levels, the parameters of the transformer and a power grid are converted to the primary side, the transformer is simplified into an equivalent inductor, the filter and the transformer are integrally regarded as an LCL filter, and the mathematical model is as follows:
in the formula, L f Is filter inductance, i f For the current flowing through the filter inductance, i fd 、i fq The components of the filter inductance current in d and q axes of a synchronous rotating coordinate system, C f Is a filter capacitance, v cf Is the filter capacitor voltage, v cfd 、v cfq The components of the filter capacitor voltage in the synchronous rotation system of d and q axes, R f 、R c Parasitic resistances, L, of the filter inductance and the filter capacitance, respectively t Is an equivalent inductance of a transformer, v pcc To the grid point voltage, v pccd 、v pccq Respectively d-axis component and q-axis component, i, of the grid-connected point voltage in a synchronous rotation coordinate system t For the current through the equivalent inductance of the transformer, i td 、i tq Respectively representing d-axis components and q-axis components of the equivalent inductive current of the transformer under a synchronous rotating coordinate system, wherein omega is the angular frequency of a power grid;
s15, a maximum power point tracking controller and a mathematical model of a grid-connected voltage and current controller:
the maximum power point tracking controller is used for generating the duty ratio of a preceding stage Boost circuit and the photovoltaic output voltage v pv Voltage value v corresponding to maximum power point mp Comparing, inputting error signal into PI controller to generate duty ratio d of preceding stage Boost circuit, and mathematical expression thereofComprises the following steps:
in the formula: k is a radical of po 、k io Proportional gain and integral gain of the voltage outer loop PI controller are respectively, and s is a Laplace operator;
the controller of the grid-connected inverter consists of a voltage outer ring and a current inner ring, wherein the voltage outer ring is used for stabilizing the voltage v of the direct-current bus dc The current inner ring is used for improving the dynamic response of grid-connected current and ensuring that the grid-connected current is connected in a unit factor mode, and the mathematical models of the voltage outer ring and the current inner ring are as follows:
in the formula:
is d-axis and q-axis current reference values under a synchronous rotating coordinate system,
is the reference value of the DC bus voltage, k pdc 、k idc Respectively, the proportional and integral coefficients, m, of the voltage outer loop PI controller d 、m q The modulation degrees, k, of the inverter under d and q axes in a synchronous rotation coordinate system pd 、k id Respectively is the proportional coefficient and the integral coefficient k of a d-axis current inner loop PI controller under a synchronous rotating coordinate system pq 、k iq The proportional and integral coefficients of the q-axis current inner loop PI controller under the synchronous rotation coordinate system are respectively.
2. The structure-preserving-method-based large-scale photovoltaic power generation system aggregation equivalence method according to claim 1, wherein the relationship between the magnetic field energy and the electric field energy of any two parallel photovoltaic power generation units and the energy conservation in the system in S2 is specifically expressed as follows:
in the formula: t represents magnetic field energy, V represents electric field energy, k is a constant, U represents generalized potential energy in a photovoltaic system, wherein the generalized potential energy of the photovoltaic system consists of output energy of an alternating current power supply, input energy of a direct current power supply and energy consumed by a resistor in the system, and digital subscripts 1 and 2 are used for distinguishing main circuit parameters of any two photovoltaic power generation units connected in parallel;
the relationship between the state variables can be obtained from the energy conservation relationship in equation (19), which is expressed as follows:
in the formula: k is a radical of L The numerical subscripts 1 and 2 are used for distinguishing main circuit parameters of any two photovoltaic power generation units connected in parallel.
3. The structure maintaining method-based large-scale photovoltaic power generation system aggregation equivalence method according to claim 2, wherein S3 a current-voltage relationship between the detailed model and the equivalent model, specifically, a power level in the photovoltaic system is determined by a grid-connected current, and in order to maintain the same active power between the equivalent model and the detailed model, the power of the equivalent model is a sum of powers of the photovoltaic power generation units in the detailed model, so that a current relationship between the equivalent model and the detailed model can be obtained, and a mathematical expression thereof is:
in the formula: i.e. i pveq Is the output current of the photovoltaic array in the equivalence model, i Leq For storing inductor current, i, of Boost circuit in equivalent model dceq For the inverter input current, i, in the equivalence model feq For the current, i, of the filter inductor in the equivalent model teq Is the current i flowing through the equivalent inductance of the transformer in the equivalent model pvl 、i Ll 、i dcl 、i fl 、i tl Respectively outputting current of a photovoltaic array in the first parallel power generation unit in the large-scale photovoltaic system, energy storage inductive current of a Boost circuit, input current of an inverter, inductive current of a filter and equivalent inductive current of a transformer, wherein l is any number in the range of 1-n, and n is the number of the parallel power generation units in the large-scale photovoltaic system;
according to the detailed model and the equivalent model, the same voltage class power distribution network is accessed through the same power transmission line, the first side and the second side of the transformer in each photovoltaic power generation unit have the same voltage class, the voltage relation between the equivalent model and the detailed model is obtained, and the mathematical expression is as follows:
v pcceq ＝v pccl (22)
in the formula, v pcceq Representing the voltage of a grid-connected point in an aggregate equivalence model, v pccl The grid-connected point voltage of the first power generation unit in the large-scale photovoltaic power generation system;
according to the voltage proportional relation in the formula (20), the rest voltage relation between the polymerization model and the detailed model can be obtained, and the mathematical expression thereof is as follows:
v pveq ＝v pvl ,v dceq ＝v dcl ,v cfeq ＝v cfl · (23)
in the formula: v. of pveq Is the output voltage, v, of the photovoltaic array in the equivalence model dceq In an equivalent modelDC bus voltage, v cfeq For the filter capacitor voltage, v, in the equivalent model pvl 、v dcl 、v cfl Respectively outputting voltage, direct current bus voltage and filter capacitor voltage for a photovoltaic array in the first parallel power generation unit in a large-scale photovoltaic system;
according to the voltage-current relation mathematical expression of the detailed model and the equivalent model, each photovoltaic power generation unit in the detailed model and the equivalent model have the same photovoltaic array output voltage, direct-current bus voltage, filter capacitor voltage and primary side equivalent grid voltage, and the output current of the photovoltaic array, the energy storage inductive current of the Boost circuit, the input current of the inverter, the inductive current of the filter and the current flowing through the transformer in the aggregation model are the sum of the corresponding currents of each photovoltaic power generation unit in the detailed model respectively.
4. The structure-keeping-method-based large-scale photovoltaic power generation system aggregation equivalent method as claimed in claim 3, wherein the state equation of the photovoltaic power generation system aggregation equivalent model is established in step S4, and the method comprises the following steps:
s41, a preceding stage Boost circuit, an inverter and a mathematical model of a filter in the aggregation model:
according to the two-stage photovoltaic power generation system state equation established in the step S1, the state equation of the aggregation equivalent model is obtained by popularization, and the mathematical expression is as follows:
in the formula: c pveq Is a preceding stage filter capacitor in an equivalent model, L eq For Boost circuit energy storage inductance in equivalent model, d eq Is the duty ratio of Boost circuit in equivalent model, C dceq Is a DC bus capacitor in an equivalent model, L feq Is a filter inductance in an equivalent model, S abceq As a switching function of an equivalent inverter, C feq As filter capacitance in the equivalent model, R feq Is parasitic resistance, R, of filter inductor in equivalent model ceq Is an equivalent modeType medium filter capacitor parasitic resistance, L teq Equivalent inductance of the transformer in the equivalent model;
s42, controller model in the aggregation model:
by popularizing the formula (15), the maximum power point tracking controller model of the aggregate equivalent model can be obtained, and the mathematical expression of the model is as follows:
d eq ＝k poeq (v mpeq -v pveq )+k ioeq ∫(v mpeq -v pveq )dt (25)
in the formula, k poeq Representing the equivalent proportionality coefficient, k, of the Boost circuit PI controller in the equivalent model ioeq Represents the equivalent integral coefficient v of the Boost circuit PI controller in the equivalent model mpeq The maximum voltage corresponding to the maximum power point in the equivalent model;
similarly, a grid-connected voltage and current controller model in the aggregate equivalence model can be obtained, and the mathematical expression of the grid-connected voltage and current controller model is as follows:
in the formula:
are d-axis and q-axis current reference values i in the equivalent model respectively tdeq 、i tqeq Are respectively d-axis components and q-axis components of equivalent inductance current of the transformer in the equivalent model,
is a direct current bus in an equivalent modelLine voltage reference value, k pdceq 、k idceq Respectively is the proportional coefficient and the integral coefficient m of a voltage outer ring PI controller in the equivalent model deq 、m qeq Respectively the modulation degree of d and q axes of the inverter synchronous rotation coordinate system in the equivalent model, k pdeq 、k ideq Are respectively proportional and integral coefficients, k, of a d-axis current inner loop PI controller in an equivalent model pqeq 、k iqeq And the proportional coefficient and the integral coefficient of the q-axis current inner loop PI controller in the equivalent model are respectively.
5. The structure keeping method-based aggregation equivalence method for large-scale photovoltaic power generation systems according to claim 4, wherein in the step S5, aggregation parameter calculation formulas of a photovoltaic array, a Boost circuit, a grid-connected inverter, a filter, a transformer, a maximum power point tracking controller and a grid-connected voltage and current controller in the equivalent model are established, and the method comprises the following steps:
s51, an equivalent photovoltaic array calculation method in the aggregation model:
the output voltage of the photovoltaic array is mainly determined by the serial number, the output current is mainly determined by the parallel number, the output voltage of the photovoltaic array in the equivalent model and the detailed model is unchanged, the output current of the photovoltaic array in the equivalent model is the sum of the output currents of the photovoltaic arrays in parallel connection with the detailed model, and therefore the calculation formula of the equivalent photovoltaic array is obtained:
in the formula: n is a radical of seq Is the serial number of equivalent photovoltaic arrays, N peq The number of the equivalent photovoltaic arrays in parallel is the same as that of the detailed model photovoltaic arrays in the aggregation equivalent model, namely the number of the equivalent photovoltaic arrays in series is the sum of the number of the detailed model photovoltaic arrays in parallel;
s52, a method for calculating the aggregation parameters of the medium value Boost circuit, the equivalent inverter and the equivalent filter in the aggregation model comprises the following steps:
according to the mathematical model of the large-scale photovoltaic system of the two-stage photovoltaic power generation system, the mathematical model of the front-stage boost circuit, the inverter and the filter in any parallel photovoltaic power generation unit can be obtained, and the mathematical expression is as follows:
in the formula: c pvl Is the preceding stage filter capacitor, L, of the first parallel power generation unit in a large-scale photovoltaic system l Energy storage inductor d for Boost circuit of the first parallel power generation unit in large-scale photovoltaic system l Is the duty ratio of Boost circuit in equivalent model, C dcl Is the direct current bus capacitor, L of the first parallel power generation unit in a large-scale photovoltaic system fl Is the filter inductance of the first parallel power generation unit in a large-scale photovoltaic system S abcl For the switching function of the first parallel power generating unit in large-scale photovoltaic systems, C fl Is the filter capacitor R of the first parallel power generation unit in a large-scale photovoltaic system fl Is the filter inductance parasitic resistance R of the first parallel power generation unit in a large-scale photovoltaic system cl The filter capacitance parasitic resistance L of the first parallel power generation unit in a large-scale photovoltaic system tl Equivalent inductance of a transformer of the first parallel power generation unit in a large-scale photovoltaic system;
the state equations of a Boost circuit, an inverter and a filter of n photovoltaic power generation units connected in parallel are superposed, and the mathematical expression is as follows:
supposing that each Boost circuit in each photovoltaic power generation unit has no difference in inverter control and uses carrier waves with the same frequency, because the inverter is connected to a power distribution network with the same voltage level, and the photovoltaic array output voltage, the direct current bus voltage and the grid-connected point voltage in each photovoltaic power generation unit are the same as those in the equivalent model, the duty ratio of each Boost circuit in each parallel power generation unit of the detailed model and the equivalent model is the same as that of the inverter, the switching function of the inverter is also the same, and the mathematical expression is as follows:
S abceq ＝S abcl ,d eq ＝d l (32)
from the result of equation (32), comparing the left side of equation (24) and equation (31), the method for calculating the equivalent inductance and equivalent capacitance in the equivalent model is known, and the mathematical expression is:
by using the obtained equivalent capacitance and equivalent inductance calculation formula and comparing the right terms of the formula (24) and the formula (31), the calculation method of the equivalent resistance in the equivalent model can be known, and the mathematical expression is as follows:
s53, a method for calculating equivalent parameters of the transformer in the equivalent model comprises the following steps:
in order to keep the primary side voltage of the transformer unchanged after equivalence, the equivalent transformer capacity in the equivalent model is the sum of the capacities of all transformers in the detailed model, and the mathematical expression is as follows:
in the formula: s teq For the transformer capacity, S, in the equivalent model tl The capacity of a transformer of the first parallel power generation unit in the large-scale photovoltaic power generation system;
s54, a controller equivalent parameter calculation method in the equivalent model comprises the following steps:
the equivalent model and the detailed model have the same main circuit structure and control circuit structure, the output voltage of a photovoltaic array in the equivalent model and the duty ratio of a Boost circuit in the equivalent model are the same as those of the detailed model, and the equivalent parameter calculation method for obtaining the maximum power point tracking PI controller in the equivalent model by comparing the formula (15) with the formula (25) is as follows:
k poeq ＝k pol ,k ioeq ＝k iol (36)
in the formula: k is a radical of formula pol Proportional coefficient k of a Boost circuit PI controller of the first parallel power generation unit in a large-scale photovoltaic system iol The integral coefficient of a Boost circuit PI controller of the first parallel power generation unit in the large-scale photovoltaic system is obtained;
according to the method, the grid-connected current in the photovoltaic system mainly determines the output active power of the photovoltaic system, the same direct-current bus voltage is provided for the detailed model and the equivalent model, the detailed model and the equivalent model have the same voltage reference signal, in order to ensure that the detailed model and the equivalent model have the same active power, a d-axis current reference value signal representing the active current in the equivalent model is the sum of d-axis current reference values in the detailed model, and the mathematical expression is as follows:
in the formula:
a d-axis current reference signal of the first generating unit in the large-scale photovoltaic system;
according to the result of the equation (37), comparing the equation (16) with the equation (26), the equivalent parameter calculation method of the inverter voltage outer loop in the equivalent model can be obtained, and the mathematical expression is as follows:
in the formula: k is a radical of formula pdcl For voltage outer loop PI control of the first parallel power generation unit in a large-scale photovoltaic systemProportionality coefficient of device, k idcl The integral coefficient of a voltage outer loop PI controller of the first parallel power generation unit in the large-scale photovoltaic system is obtained;
the detailed model and the equivalent model have the same active power, and the equivalent current inner loop controller parameters are calculated by adopting a capacity weighting method, specifically, a capacity weighting factor gamma is defined l The mathematical expression is as follows:
in the formula: p l The active output, P, of the first power generation unit in the large-scale photovoltaic power generation system sum The total active power output of the large-scale photovoltaic system;
further, an equivalent PI parameter calculation method of the current inner loop controller in the equivalent aggregation model can be obtained, and the mathematical expression is as follows:
in the formula: k is a radical of formula pdl D-axis current inner loop PI controller proportionality coefficient k representing the first parallel power generation unit in large-scale photovoltaic system idl D-axis current inner loop PI controller integral coefficient k representing the first parallel power generation unit in a large-scale photovoltaic system pql Q-axis current inner loop PI controller proportionality coefficient k representing the first parallel power generation unit in large-scale photovoltaic system iql And the integral coefficient of the q-axis current inner loop PI controller of the ith parallel power generation unit in the large-scale photovoltaic system is represented.
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